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Short Diagonal of Trapezoid given Height Formula

GoShort Diagonal of Trapezoid Formula

GoShort Diagonal of Trapezoid given Short Leg Formula

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Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid. Check FAQs

d Short = \sqrt{h^{2} + {(B Long - (h \cdot \cot (∠ Smaller Acute)))}^{2}}

d_Short - Short Diagonal of Trapezoid?h - Height of Trapezoid?B_Long - Long Base of Trapezoid?∠_{Smaller Acute} - Smaller Acute Angle of Trapezoid?

Short Diagonal of Trapezoid given Height Example

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Here is how the Short Diagonal of Trapezoid given Height equation looks like with Values.

Here is how the Short Diagonal of Trapezoid given Height equation looks like with Units.

Here is how the Short Diagonal of Trapezoid given Height equation looks like.

11.5186 = \sqrt{8^{2} + {(15 - (8 \cdot \cot (50)))}^{2}}

11.5186m = \sqrt{{8m}^{2} + {(15m - (8m \cdot \cot (50°)))}^{2}}

11.5186 = \sqrt{8^{2} + {(15 - (8 \cdot \cot (50)))}^{2}}

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Short Diagonal of Trapezoid given Height Solution

Follow our step by step solution on how to calculate Short Diagonal of Trapezoid given Height?

FIRST Step Consider the formula

d Short = \sqrt{h^{2} + {(B Long - (h \cdot \cot (∠ Smaller Acute)))}^{2}}

Next Step Substitute values of Variables

∴

d Short = \sqrt{{8m}^{2} + {(15m - (8m \cdot \cot (50°)))}^{2}}

Next Step Convert Units

∴

d Short = \sqrt{{8m}^{2} + {(15m - (8m \cdot \cot (0.8727rad)))}^{2}}

Next Step Prepare to Evaluate

∴

d Short = \sqrt{8^{2} + {(15 - (8 \cdot \cot (0.8727)))}^{2}}

Next Step Evaluate

∴

d Short = 11.5185820630881m

LAST Step Rounding Answer

∴

d Short = 11.5186m

Short Diagonal of Trapezoid given Height Formula Elements

Variables

Functions

Short Diagonal of Trapezoid

Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid.

Symbol: d_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Diagonal of Trapezoid

Height of Trapezoid

Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Trapezoid

Long Base of Trapezoid

Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.

Symbol: B_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Base of Trapezoid

Smaller Acute Angle of Trapezoid

Smaller Acute Angle of Trapezoid is the smaller angle on the long base or the angle made by the long base and long leg of the Trapezoid.

Symbol: ∠_{Smaller Acute}

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Smaller Acute Angle of Trapezoid

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Short Diagonal of Trapezoid

Go Short Diagonal of Trapezoid

d Short = \sqrt{{B Long}^{2} + {L Long}^{2} - (2 \cdot B Long \cdot L Long \cdot \cos (∠ Smaller Acute))}

Go Short Diagonal of Trapezoid given Short Leg

d Short = \sqrt{{B Short}^{2} + {L Short}^{2} - (2 \cdot B Short \cdot L Short \cdot \cos (∠ Smaller Obtuse))}

Go Short Diagonal of Trapezoid given all Sides

d Short = \sqrt{{L Long}^{2} + (B Short \cdot B Long) - (B Long \cdot \frac{{L Long}^{2} - {L Short}^{2}}{B Long - B Short})}

Go Short Diagonal of Trapezoid given Height and Larger Acute Angle

d Short = \sqrt{h^{2} + {(B Short + (h \cdot \cot (∠ Larger Acute)))}^{2}}

How to Evaluate Short Diagonal of Trapezoid given Height?

Short Diagonal of Trapezoid given Height evaluator uses Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2) to evaluate the Short Diagonal of Trapezoid, Short Diagonal of Trapezoid given Height formula is defined as the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid, and calculated using height of the Trapezoid. Short Diagonal of Trapezoid is denoted by d_Short symbol.

How to evaluate Short Diagonal of Trapezoid given Height using this online evaluator? To use this online evaluator for Short Diagonal of Trapezoid given Height, enter Height of Trapezoid (h), Long Base of Trapezoid (B_Long) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) and hit the calculate button.

FAQs on Short Diagonal of Trapezoid given Height

What is the formula to find Short Diagonal of Trapezoid given Height?

The formula of Short Diagonal of Trapezoid given Height is expressed as Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). Here is an example- 11.51858 = sqrt(8^2+(15-(8*cot(0.872664625997001)))^2).

How to calculate Short Diagonal of Trapezoid given Height?

With Height of Trapezoid (h), Long Base of Trapezoid (B_Long) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) we can find Short Diagonal of Trapezoid given Height using the formula - Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). This formula also uses Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Short Diagonal of Trapezoid?

Here are the different ways to Calculate Short Diagonal of Trapezoid-

Short Diagonal of Trapezoid=sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*Long Leg of Trapezoid*cos(Smaller Acute Angle of Trapezoid)))
Short Diagonal of Trapezoid=sqrt(Short Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Short Base of Trapezoid*Short Leg of Trapezoid*cos(Smaller Obtuse Angle of Trapezoid)))
Short Diagonal of Trapezoid=sqrt(Long Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Long Leg of Trapezoid^2-Short Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid)))

Can the Short Diagonal of Trapezoid given Height be negative?

No, the Short Diagonal of Trapezoid given Height, measured in Length cannot be negative.

Which unit is used to measure Short Diagonal of Trapezoid given Height?

Short Diagonal of Trapezoid given Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Short Diagonal of Trapezoid given Height can be measured.

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Short Diagonal of Trapezoid given Height Formula

​GoShort Diagonal of Trapezoid Formula

​GoShort Diagonal of Trapezoid given Short Leg Formula

Short Diagonal of Trapezoid given Height Example

Short Diagonal of Trapezoid given Height Solution

Short Diagonal of Trapezoid given Height Formula Elements

Other Formulas to find Short Diagonal of Trapezoid

How to Evaluate Short Diagonal of Trapezoid given Height?

FAQs on Short Diagonal of Trapezoid given Height

Variable Name

GoShort Diagonal of Trapezoid Formula

GoShort Diagonal of Trapezoid given Short Leg Formula